{
  "id": "0908.2537",
  "version": "v3",
  "published": "2009-08-18T10:10:25.000Z",
  "updated": "2010-07-26T15:08:30.000Z",
  "title": "On the Facets of the Secondary Polytope",
  "authors": [
    "Sven Herrmann"
  ],
  "comment": "28 pages, 18 figures",
  "journal": "Journal of Combinatorial Theory, Series A, 118 (2011), no.2, 425-447",
  "doi": "10.1016/j.jcta.2010.08.003",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "The secondary polytope of a point configuration A is a polytope whose face poset is isomorphic to the poset of all regular subdivisions of A. While the vertices of the secondary polytope - corresponding to the triangulations of A - are very well studied, there is not much known about the facets of the secondary polytope. The splits of a polytope, subdivisions with exactly two maximal faces, are the simplest examples of such facets and the first that were systematically investigated. The present paper can be seen as a continuation of these studies and as a starting point of an examination of the subdivisions corresponding to the facets of the secondary polytope in general. As a special case, the notion of k-split is introduced as a possibility to classify polytopes in accordance to the complexity of the facets of their secondary polytopes. An application to matroid subdivisions of hypersimplices and tropical geometry is given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-07-26T15:08:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B30",
      "52B40",
      "52B11",
      "52B35"
    ],
    "keywords": [
      "secondary polytope",
      "face poset",
      "matroid subdivisions",
      "regular subdivisions",
      "maximal faces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2537H"
    }
  }
}